Simulation-aided investigation of beam hardening induced errors in CT dimensional metrology

Industrial x-ray computed tomography (CT) systems are being increasingly used as dimensional measuring machines. However, micron level accuracy is not always achievable, as of yet. The measurement accuracy is influenced by many factors, such as the workpiece properties, x-ray voltage, filter, beam hardening, scattering and calibration methods (Kruth et al 2011 CIRP Ann. Manuf. Technol. 60 821–42, Bartscher et al 2007 CIRP Ann. Manuf. Technol. 56 495–8, De Chiffre et al 2005 CIRP Ann. Manuf. Technol. 54 479–82, Schmitt and Niggemann 2010 Meas. Sci. Technol. 21 054008). Since most of these factors are mutually correlated, it remains challenging to interpret measurement results and to identify the distinct error sources. Since simulations allow isolating the different affecting factors, they form a useful complement to experimental investigations. Dewulf et al (2012 CIRP Ann. Manuf. Technol. 61 495–8) investigated the influence of beam hardening correction parameters on the diameter of a calibrated steel pin in different experimental set-ups. It was clearly shown that an inappropriate beam hardening correction can result in significant dimensional errors. This paper confirms these results using simulations of a pin surrounded by a stepped cylinder: a clear discontinuity in the measured diameter of the inner pin is observed where it enters the surrounding material. The results are expanded with an investigation of the beam hardening effect on the measurement results for both inner and outer diameters of the surrounding stepped cylinder. Accuracy as well as the effect on the uncertainty determination is discussed. The results are compared with simulations using monochromatic beams in order to have a benchmark which excludes beam hardening effects and x-ray scattering. Furthermore, based on the above results, the authors propose a case-dependent calibration artefact for beam hardening correction and edge offset determination. In the final part of the paper, the investigations are expanded with experiments of a new set-up that includes non-cylindrical features; the effectiveness of the proposed calibration artefact is also studied.